|
Search: id:A132969
|
|
|
| A132969 |
|
Expansion of phi(q) * chi(q) in powers of q where phi(), chi() are Ramanujan theta functions. |
|
+0
2
|
|
| 1, 3, 2, 1, 5, 5, 3, 5, 6, 10, 10, 8, 13, 15, 15, 16, 23, 27, 25, 30, 35, 40, 42, 45, 55, 66, 68, 70, 86, 95, 100, 110, 125, 141, 150, 161, 185, 207, 215, 235, 266, 293, 310, 335, 375, 410, 438, 470, 521, 575, 610, 653, 725, 785, 835, 900, 983, 1070, 1140, 1220, 1331
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; top of p. 60.
|
|
FORMULA
|
Expansion of phi(q) + 2 * psi(q) in powers of q where phi(), psi() are Ramanujan 3rd order mock theta functions.
Expansion of q^(1/24) * eta(q^2)^7 / ( eta(q) * eta(q^4) )^3 in powers of q.
Euler transform of period 4 sequence [ 3, -4, 3, -1, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (2304 t)) = 48^(1/2) (t/i)^(1/2) f(t) where q = exp(2 pi i t).
G.f.: ( Sum_{k} x^k^2 ) * ( Product_{k>0} (1 + x^(2*k-1)) ).
G.f.: Product_{k>0} (1 - x^(2*k)) * ( (1 + x^k) / (1 + x^(2*k)) )^3.
|
|
EXAMPLE
|
1/q + 3*q^23 + 2*q^47 + q^71 + 5*q^95 + 5*q^119 + 3*q^143 + 5*q^167 +...
|
|
PROGRAM
|
(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, (n+1)\2, 1 + x^(2*k-1), 1 + x*O(x^n)) * sum(k=1, sqrtint(n), 2 * x^k^2, 1), n))}
(PARI) {a(n) = local(A) ; if( n<0, 0, A = x * O(x^n) ; polcoeff( eta(x^2 + A)^7 / ( eta(x + A) * eta(x^4 + A) )^3, n))}
|
|
CROSSREFS
|
A132970(n) = (-1)^n * a(n). A124226(n) = (-1)^n * a(n) unless n=1.
Sequence in context: A068389 A091597 A091595 this_sequence A132970 A139377 A110712
Adjacent sequences: A132966 A132967 A132968 this_sequence A132970 A132971 A132972
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Michael Somos, Sep 04 2007
|
|
|
Search completed in 0.002 seconds
|
